Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there. In this slide the discussed points are: 1. Dispersion & it's types 2. Definition 3. Use 4. Merits 5. Demerits 6. Formula & math 7. Graph and pictures 8. Real life application.

1. Measure of
Dispersion

2. We are Group 4
Tasnim Ansari Hridi (ID-09)
Md. Mehedi Hassan Bappy (ID-21)
Debanik Chakraborty (ID-25)
Syed Ishtiak Uddin Ahmed (ID-31)
Devasish Kaiser (ID-49)

3. Definition of Measure of Dispersion
In statistics, dispersion (also called
variability, scatter, or spread) is the extent
to which a distribution is stretched or
squeezed. Common examples
of measures of statistical dispersion are the
variance, standard deviation, and
interquartile range.

4. Example
Centre: Same
Variation: Different
Year 2000: Close Dispersion
Year 2015: Wide Dispersion
Better Quality Data:Data ofYear 2000

5. Why Measure of Dispersion
Serve as a basis for the
control of the variability
To compare the variability
of two or more series

6. Facilitate the use of other
statistical measures.
Reliable
Determine the reliability of
an average
Why Measure of Dispersion

7. Characteristics of an Ideal
Measure of Dispersion
 Must be based on all observations of the data.
 It should be rigidly defined
 It should be easy to understand and calculate.

8.  Must be least affected by the sampling
fluctuation.
 Must be easily subjected to further mathematical
operations
Characteristics of an Ideal
Measure of Dispersion
 It should not be unduly affected by the extreme
values.

9. Types of Measures of
Dispersion

10. Classification of
Measures of dispersion
in Statistics

11. Measures
of
Dispersion
Algebraic
Absolute Relative
Graphical

12. Algebraic Measure of Dispersion
× Mathematical way to calculate the
measure of dispersion.
Example: Calculation of Standard Deviation
or Co-efficient of Variance by using numbers
and formulas.

13. Characteristics of Algebraic
Measure of Dispersion
• Mathematical Way
• Algebraic Variables are used
• Numerical Figures are used here
• Formulas & Equations are used

14. Graphical Measure of Dispersion
× The way to calculate the measure of
dispersion by figures and graphs.
Example: Calculation of Dispersion among
the heights of the students of a class from
the average height using a graph.

15. Characteristics of Graphical
Measure of Dispersion
• It is a visual way of measuring dispersion
• Graphs, figures are used
• Sometimes, it cannot give the actual result
• It helps the reader to have an idea about the
dispersion practically at a glance

16. Absolute Measure of Dispersion
Absolute Measure of Dispersion gives an idea about the
amount of dispersion/ spread in a set of observations. These
quantities measures the dispersion in the same units as the
units of original data. Absolute measures cannot be used to
compare the variation of two or more series/ data set.

17. Classification of
Algebraic Measure of
Dispersion

18. Absolute Measure of
Dispersion
Absolute Measure of Dispersion gives an idea about the
amount of dispersion/ spread in a set of observations. These
quantities measures the dispersion in the same units as the
units of original data. Absolute measures cannot be used to
compare the variation of two or more series/ data set.

19. Relative Measure of Dispersion
These measures are a sort of ratio and are called coefficients.
Each absolute measure of dispersion can be converted into
its relative measure.
It can be used to compare two or more data sets

20. Difference Between Absolute and Relative Measure of
Dispersion
3
This is calculated from original data
These measure are calculated absolute
measures
2
It is not expressed in terms of percentage It is expressed in terms of percentage
1
It has the variable unit It has no unit
Absolute Measure Relative Measure

21. 6
There is no change in variables and with the
absolute measures.
There is changes in variables with relative
measures.
5
These measure cannot be used to compare the
variation of two or more series
These measure can be used to compare the
variation of two or more series.
4
No use of ratio Use of ratio
Absolute Measure Relative Measures

22. Absolute
measures of
Dispersion

23. Classification of Absolute measure
Mean Deviation
Quartile Deviation Standard Deviation
Range

24. “
Range

25. Range
The difference between the maximum and
minimum observations in the data set.
R= H-L

26. 5, 10 , 15 , 20, 7, 9, 12 , 17 , 13 , 6 , 10 , 11
, 17 , 16
Range = H- L
= 20- 5 = 15

27. Merits and Demerits of Range
Gives a quick answer
Cannot be calculated in open ended
distributions
Affected by sampling fluctuations
Changes from one sample to the
next in population
Gives a rough answer and is not
based on all observationSimple and easy to
understand

28. “
Mean deviation

29. Mean deviation
The average of the absolute values of
deviation from the mean(median or mode) is
called mean deviation.
 =
𝒇 | 𝒙 − 𝒙 |
𝑵

30. Merits of Mean deviation
Simplifies
calculations
Can be
calculated by
mean, median
and mode
Is not affected
by extreme
measures
Used to make
healthy
comparisons

31. Demerits of Mean Deviation
Not reliable
Mathematically
illogical to
assume all
negatives as
positives
Not suitable for
comparing
series

32. “
Quartile Deviation

33. Quartile Deviation
The half distance
between 75th
percentile i.e. 3rd
quartile (Q1) and 25th
percentile i.e. 1st
quartile (Q3) is
Quartile deviation or
Interquartile range.
Q.D =
Q3 – Q1
𝟐

34. Has better result than
range mode.
Is not affected by
extreme items
Merits of Quartile Deviation

35. Demerits of Quartile Deviation
It is completelydependent on thecentral items.
All the items of the frequencydistribution are not given
equal importance in finding the values of Q1 and Q3
Because it does not take into accountall the items of the
series, considered to be inaccurate.

36. “
Standard Deviation

37. Standard Deviation
Standard deviation is calculated as the
square root of average of squared
deviations taken from actual mean.
It is also called root mean square
deviation.
 = √
𝒙− 𝒙
𝟐
𝒏

38. 68.2%
95.4%
99.7%

39. Merits of standard deviation
It takes intoaccount all the items and is capableof future
algebraic treatment andstatistical analysis.
It is possible to calculatestandard deviationfor two or more
series
This measure is most suitable for makingcomparisonsamong
two or more series about variability.

40. Demerits of Standard Deviation
It is difficult to
compute. It assigns more
weights to extreme
itemsand less
weights to items
that are nearer to
mean.

41. Classifications of
Relative Measures of
Dispersion

42. Chart of classification
Relative
Measure
Coefficient of
Range
Coefficient of
Quartile
Deviation
Coefficient of
Mean
Deviation
Coefficient of
Variation

43. Coefficient
of
Range

44. Coefficient of Range
The measure of the distribution based on range
is the coefficient of range also known as range
coefficient of dispersion.
Formula:
Coefficient of Range=
𝑅𝑎𝑛𝑔𝑒
𝐻𝑖𝑔ℎ𝑒𝑠𝑡 𝑉𝑎𝑙𝑢𝑒+𝐿𝑜𝑤𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒
× 100

45. “Coefficient
of
Quartile Deviation

46. Coefficient of Quartile Deviation
A relative measure of dispersion based on the
quartile deviation is called the coefficient of
quartile deviation.
Formula:
Coefficient of Quartile Deviation =
𝑄𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑀𝑒𝑑𝑖𝑎𝑛
× 100
=
Q3 – Q1
Q3 + Q1
× 100 [By Simplification]

47. Merits & Demerits of Coefficient of Quartile
Deviation
Merits
1. Easily understood
2. Not much Mathematical
Difficulties
3. Better Result than
Coefficient of Range
 Sampling fluctuation
 Ignorance of last 25%
of data sets.
 Values being irregular
Demerits

48. Coefficient
of
Mean Deviation

49. Coefficient of Mean Deviation
The relative measure of dispersion we get by dividing
Mean Deviation by Mean or Median, is called Coefficient
of Mean Deviation.
Formula:
Coefficient of MD=
𝑀𝑒𝑎𝑛 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑀𝑒𝑑𝑖𝑎𝑛 𝑜𝑟 𝑀𝑒𝑎𝑛
× 100

50. Merits & Demerits of Coefficient of Mean
Deviation
Merits
1. Better Result than Range
& Quartile Coefficient.
2. Least sampling fluctuation.
3. Rigidly defined.
 Fractional Average.
 Cannot be used for
sociological studies
 Less reliable than
Coefficient of Variation
Demerits

51. Coefficient
of
Variation

52. Coefficient of Variation
Coefficient of Variation is a measure of spread
that describes the amount of variability relative to
the mean.
Formula:
Coefficient of Variation=
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑀𝑒𝑎𝑛
× 100

53. Merits & Demerits of Coefficient of Variation
Merits
1. Best one
2. Most appropriate one
3. Based on Mean and
Standard Deviation
4. COV is dimensionless or non-
unitized
 It is impossible to calculate if
Mean is 0
 It is difficult to calculate if
the values are both positive
and negative numbers & if
the mean is close to 0.
Demerits

54. Practical Uses of Coefficient of Variance
INVESTMENT ANALYSIS
STOCK MARKET
RISK EVALUATION
COMBINED STANDARD DEVIATION OF SEVERAL GROUPS
PERFORMANCES OF TWO PLAYERS
INDUSTRIES & FACTORIES

55. Mathematical
Application

56. Coefficient of range
Let 1,2,4,6,7 is a set of values of a distribution.
Here, Highest Value, XH=7 &
Lowest Value, XL=1
So, Range, R= 7-1 = 6
Now, Coefficient of Range =
𝐑
XH + XL
× 100
=
𝟔
𝟕+𝟏
× 100 =75%

57. Coefficient of Quartile
deviationLet the number of students in 5 classes are 110, 150, 180, 190, 240
is a set of values.
Here, Q1= size of
𝐍+𝟏
𝟒
th item = 130
And, Q3 = size of
𝟑(𝐍+𝟏)
𝟒
th item = 215
So, Coefficient of Quartile Deviation =Q3 – Q1
Q3 + Q1
× 100
= 215−130
215+130
× 100= 24.64 %

58. Coefficient of Mean Deviation
Let the ages of 5 boys in a class is 12, 14, 14, 15, 18.
So their Mean, 𝐱 =
𝟏𝟐+𝟏𝟒+𝟏𝟒+𝟏𝟓+𝟏𝟖
𝟓
= 14.6
Mean Deviation, MD =
| 𝒙 − 𝒙 |
𝑵
=|12−14.6| + |14−14.6| + |14− 14.6|+ |15−14.6| + |18−14.6|
𝟓
= 1.52
Now, the Coefficient of MD=
𝐌𝐃
𝐱
× 𝟏𝟎𝟎 =
𝟏.𝟓𝟐
𝟏𝟒.𝟔
× 𝟏𝟎𝟎 = 10.41%

59. Coefficient of
VariationSuppose the returns on an investment for 4 years is Tk.1000,
Tk.3000, Tk.4500 & Tk.5000.
So, Mean, 𝐱 = 3375
Standard Deviation, SD = 1796.99
So,
Coefficient of Variation, CV=
𝐒𝐃
𝐱
× 100
=
𝟏𝟕𝟗𝟔.𝟗𝟗
𝟑𝟑𝟕𝟓
× 100 = 53.24%

60. The daily sale of sugar in a certain grocery shop is
given below :
Monday Tuesday Wednesday Thursday Friday
Saturday 75 kg 120 kg 12 kg 50 kg 70.5 kg 140.5 kg
respectively.

61. “
No of Days sale of sugar
Monday 60
Tuesday 120
Wednesday 10
Thursday 50
Friday 70
Saturday 140
𝜮 𝒐𝒇 𝑫𝒂𝒚𝒔 = 𝟔 𝜮𝒙 = 𝟒𝟓𝟎
Mean, 𝑥 =
𝑥
𝑛
=
4𝟓𝟎
6
= 7𝟓

62. “
x 𝒙 𝟐
60 3600
120 14400
10 100
50 2500
70 4900
140 19600
𝜮𝒙 = 𝟒𝟓𝟎 𝜮𝒙 𝟐
= 45100
Standard deviation: 𝝈 =
𝜮𝒙 𝟐
𝒏
−
𝜮𝒙
𝒏
𝟐
=
𝟒𝟓𝟏𝟎𝟎
𝟔
−
𝟒𝟓𝟎
𝟔
𝟐
=
𝟕𝟓𝟏𝟔. 𝟔𝟔 − 𝟓𝟔𝟐𝟓 = 𝟒𝟑. 𝟒𝟗

63. Quartile Deviation
The marks of 7 students in Mathematics result are given
below :
70, 85, 92,68, 75, 96, 84
Find out-
• First Quartile Deviation
• Third Quartile Deviation

64. Quartile deviation
× First quartile
𝐐 𝟏 = 𝐬𝐢𝐳𝐞 𝐨𝐟
𝐧 + 𝟏
𝟒
𝐭𝐡
𝐢𝐭𝐞𝐦
= size of
𝟕+𝟏
𝟒
𝐭𝐡
𝐢𝐭𝐞𝐦
= size of 2nd item.
= 70
×Third Quartile
𝑸 𝟑 = 𝒔𝒊𝒛𝒆 𝒐𝒇
𝟑 𝒏 + 𝟏 𝒕𝒉
𝟒
𝒊𝒕𝒆𝒎
= size of
𝟑 𝟕+𝟏 𝒕𝒉
𝟒
𝒊𝒕𝒆𝒎
= size of 6th item
=92
Arranging the data in ascending order we get,
68,70,75,84,85,92,96

65. “
Thank you